Mark,
Below is the copy of my email sent to you on Feb 27:

I implemented scalable MatPtAP and did comparisons of three implementations using ex56.c on alcf cetus machine (this machine has small memory, 1GB/core):
- nonscalable PtAP: use an array of length PN to do dense axpy
- scalable PtAP:       do sparse axpy without use of PN array
- hypre PtAP.

The results are attached. Summary:
- nonscalable PtAP is 2x faster than scalable, 8x faster than hypre PtAP
- scalable PtAP is 4x faster than hypre PtAP
- hypre uses less memory (see job.ne399.n63.np1000.sh)

Based on above observation, I set the default PtAP algorithm as 'nonscalable'. 
When PN > local estimated nonzero of C=PtAP, then switch default to 'scalable'.
User can overwrite default.

For the case of np=8000, ne=599 (see job.ne599.n500.np8000.sh), I get
MatPtAP                   3.6224e+01 (nonscalable for small mats, scalable for larger ones)
scalable MatPtAP     4.6129e+01
hypre                        1.9389e+02 

This work in on petsc-master. Give it a try. If you encounter any problem, let me know.

Hong

On Wed, May 3, 2017 at 10:01 AM, Mark Adams <mfadams@lbl.gov> wrote:
(Hong), what is the current state of optimizing RAP for scaling?

Nate, is driving 3D elasticity problems at scaling with GAMG and we are working out performance problems. They are hitting problems at ~1.5B dof problems on a basic Cray (XC30 I think).

Thanks,
Mark